Hybrid Levenberg-Marquardt and weak constraint ensemble Kalman smoother method, Nonlinear Processes in Geophysics
Résumé
We propose to use the ensemble Kalman smoother (EnKS) as the linear least squaressolver in the Gauss–Newton method for the large nonlinear least squares in incre-mental 4DVAR. The ensemble approach is naturally parallel over the ensemble mem-bers and no tangent or adjoint operators are needed. Further, adding a regulariza-5tion term results in replacing the Gauss–Newton method, which may diverge, by theLevenberg–Marquardt method, which is known to be convergent. The regularizationis implemented efficiently as an additional observation in the EnKS. The method isillustrated on the Lorenz 63 and the two-level quasi-geostrophic model problems.
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